Xen concepts for beginners: Difference between revisions
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Sintel bot (talk | contribs) Fix <math> environments for MathJax v4 (align->aligned, etc.) |
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\begin{ | \begin{aligned} | ||
\text{cents} &= 1200 \cdot \log_{2} \left( \text{ratio} \right) \\ | \text{cents} &= 1200 \cdot \log_{2} \left( \text{ratio} \right) \\ | ||
\text{ratio} &= 2^{\left( \text{cents}/1200 \right)} | \text{ratio} &= 2^{\left( \text{cents}/1200 \right)} | ||
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* [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor third and three fourths give a subminor third, just like in 22edo. | * [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor third and three fourths give a subminor third, just like in 22edo. | ||
* [[29edo]]: First edo with a perfect fifth closer to just intonation than 12edo. The minor third is extremely close to just [[13/11]]. It offers a tuning of 7L 1s with more consonant fifths than 15edo or 22edo before it. Its diatonic scale has similar melodic properties to 17edo, although subtler. | * [[29edo]]: First edo with a perfect fifth closer to just intonation than 12edo. The minor third is extremely close to just [[13/11]]. It offers a tuning of 7L 1s with more consonant fifths than 15edo or 22edo before it. Its diatonic scale has similar melodic properties to 17edo, although subtler. | ||
* [[31edo]]: One of the most popular meantone edos. Close to historical [[quarter-comma meantone]]. Not only is its major third close to just [[5/4]], it also matches the harmonic seventh [[7/4]] well. | * [[31edo]]: One of the most popular meantone edos. Close to the historical [[quarter-comma meantone]]. Not only is its major third close to just [[5/4]], it also matches the harmonic seventh [[7/4]] well. | ||
* [[34edo]]: Good for the 5-limit (2.3.5), as it does not temper out 81/80 and has a good 5/4. Also contains all notes of 17edo. | * [[34edo]]: Good for the 5-limit (2.3.5), as it does not temper out 81/80 and has a good 5/4. Also contains all notes of 17edo. | ||
* [[36edo]]: Good for primes [[3/2|3]] and [[7/4|7]]. | * [[36edo]]: Good for primes [[3/2|3]] and [[7/4|7]]. | ||
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* [[87edo]]: Even better in 2.3.5.11.13 than 72edo is in the 11-limit, and a consistent and precise edo for approximating harmonics 8 to 16, but ratios with 7 suffer due to the 7 being flat and the 3 being sharp. | * [[87edo]]: Even better in 2.3.5.11.13 than 72edo is in the 11-limit, and a consistent and precise edo for approximating harmonics 8 to 16, but ratios with 7 suffer due to the 7 being flat and the 3 being sharp. | ||
* [[311edo]]: An edo renowned for being a good edo for the whole 41-odd-limit and quite a bit more (mainly composite) harmonics above 41. Essentially, the final boss of RTT edos. | * [[311edo]]: An edo renowned for being a good edo for the whole 41-odd-limit and quite a bit more (mainly composite) harmonics above 41. Essentially, the final boss of RTT edos. | ||
== Where to go next == | |||
The articles linked on the [[General theory]] page expand upon these concepts. | |||
[[Nick Vuci's Fundamentals of Xen]] and the other articles linked in the [[Guides]] page might also of use. | |||
[[Category:Overview]] | [[Category:Overview]] | ||
[[Category:Guides]] | |||